Question

If x and y are inversely proportional, then which one is true?
A. x1/y1 = x2/y2
B. x1/x2 = y1/y2
C. x1/x2 = y2/y1
D. x1.x2 = y1.y2​

Answer 1

Answer:

option c is correct✅

x1/x2=y2/y1

Answer 2

If x and y are inversely proportional then the correct option will be $\frac{x}{ {x}^{2} } = \frac{ {y}^{2} }{y}$ (option C).

Given,

x and y are inversely proportional.

To find,

The correct option among the four.

Solution,

The correct option will be $\frac{x}{ {x}^{2} } = \frac{ {y}^{2} }{y}$ (option C).

According to the question,

x and y are inversely proportional

It means that the value of x should be the following:

x = 1/y

Now, we will solve the options one by one.

A. x/y = x²/y²

Using the cross multiplication method,

xy² = yx²

Dividing by xy on both sides,

y = x

B. x/x² = y/y²

The variables in the denominator can be divided by their respective variables in the numerator:

1/x = 1/y

Using the cross multiplication method,

x = y

C. x/x² = y²/y

The variables in the denominator can be divided by their respective variables in the numerator on the left-hand side and the reverse of it can be done on the right-hand side:

1/x = y

Using the cross multiplication method,

xy = 1

x = 1/y

D. x.x² = y.y²

x³ = y³

Finding the cube roots of both sides,

x = y

Hence, the correct option is $\frac{x}{ {x}^{2} } = \frac{ {y}^{2} }{y}$ (option C).